Intrinsic phase-decoherence of electrons by two-level systems

The fundamental problem of phase saturation of electrons in a disordered mesoscopic system at very low temperatures is addressed. The disorder in the medium has both static and dynamic components, the latter being in the form of two-level systems (TLSs), which becomes just about the only source of inelastic scattering in the limit $T\to 0$. We propose that besides the inelastic nature of scattering from the TLSs, the phase-shift of the electrons is also affected by the nature of tunneling in the TLSs. The tunneling becomes incoherent as $T$ decreases due to increasing long-range interactions among TLSs and affects the phase coherence of electrons scattering from them. The competition between this effect, which increases as $\sim T^{-1}$, and that of the scattering rate ${\tau }_{e-TLS}^{-1}$ behaving as $\sim T$ apparently governs the phase-shift of electrons.